Why my blender animation broken after exoprt fbx?
First of all, I'm no expert in Blender at all, but I animated a bit recently and had a similar issue with broken animations when exporting an animated armature.
In particular, the jaw bone of the character jittered around whenever the character moved his head (the jaw bone was an unconnected child of the head bone).
In the end, I found no way of preventing this from happening, until I added a new bone connecting the jaw to the head, so the jaw bone is now a connected child of the new bone and the new bone is a connected child of the head bone.
So connecting the problematic bone(s) to the rest of the mesh seems to fix it and as far as I know, additional bones shouldn't be an issue when set to not-deforming.
I can only explain the initial issue with a bug or something, but I am not sure...
I just hope that this fixes your issue, too.